Presumably if they set the initial pressure at something greater than 1 atmosphere, but still within the comfort level of a human they wouldn't need to engineer the hull to withstand as much?
I agree with commentators here. This, and other deep sea stuff, is awesome. I'm fascinated that it's being done by private companies, and the competition between Cameron and Branson just adds to the awesomeness. (Branson appears to be losing badly.)
I don't believe there is any specific limit, as long as you give enough time to change the pressure gradually. However at higher pressures you need to reduce the oxygen and co2 concentrations (since at higher pressures they dissolve too easily). (You want to keep the partial pressure constant, even though the absolute pressure goes up.)
Water is roughly incompressible and ~10 meters (33 feet) of it will generate 1 atmosphere of pressure, so at 6 miles deep, I would guess even a very small safety factor would dominate any gains from pressurizing the capsule (I don't know anything about diving, but Wikipedia says that saturation diving is good down to about 150 meters, and the most extreme experiments went down to about 700 meters).
